Hi SJA,
I've found that feature really useful when you need to paste a code sample into an e-mail or anything of that sort, but the darker color schemes really don't translate well.
In many programs (Word included), you can do a Paste Special to remove the text formatting.
In SlickEdit, you can turn it off in Tools > Options > Editing > Selections. Uncheck "HTML Format" under Clipboard formats. If you have a SlickEdit version earlier than 13 or so, these instructions might not be accurate, but it should help you find the right option.
edit: Looks like Jim beat me to the post. Oh well.
Cheers,
Marty